The Day We Found the Universe - Marcia Bartusiak (2009)
Chapter 9. He Surely Looks Like the Fourth Dimension!
Astronomy was not the only field in a tumult as the nineteenth century turned into the twentieth. Physics, too, was in upheaval.
Doctors across the globe were still reeling over their newfound ability to use X rays, discovered in 1895 by the German physicist Wilhelm Röntgen, to peer inside the human body. Soon after, in Paris, Henri Becquerel accidentally stumbled upon a phenomenon, what came to be called radioactivity, when he was investigating the properties of uranium salt crystals. And in England J. J. Thomson identified the first particle smaller than an atom—the electron. In the new, topsyturvy world of quantum physics, light itself was soon imagined as either a wave or a particle, and physicists were realizing that their trusted laws of motion, dating back more than two hundred years to Isaac Newton, could not reliably gauge how light, whatever its form, whizzed through space. Using Newton's laws of gravity and motion, scientists arrived at one answer, but upon applying James Clerk Maxwell's laws of electromagnetism, they obtained a differing result. It took a rebel—a cocky kid who spurned rote learning throughout his schooling, always questioned conventional wisdom, and had an unshakable faith in his own abilities—to blaze a trail through this baffling territory, one that involved an entirely new take on space, time, gravity, and the behavior of the universe at large. Before anyone else, Albert Einstein discerned that a drastic change was needed, “the discovery of a universal formal principle,” as he put it.
This was not the iconic Einstein—the sockless, rumpled character with baggy sweater and fright-wig coiffure—but a younger, more romantic figure with alluring brown eyes and wavy dark hair. While in his twenties and thirties, he was at the height of his prowess. Among his gifts was a powerful physical instinct, almost a sixth sense for knowing how nature should work. This often involved his thinking in images, such as one that began haunting him as a teenager: If a man could keep pace with a beam of light, what would he see? Would he see the electromagnetic wave frozen in place like some glacial swell, as Newton's laws were suggesting? “It does not seem that something like that can exist!” Einstein later recalled thinking.
After pondering this issue long and hard, Einstein came to realize in 1905 that since all the laws of physics remain the same—whether you're at rest or in steady motion, sitting quietly on a beach or reading on a train—then the speed of light has to stay constant as well in both situations. He had found the answer to his question. No one can catch up with a light beam, no matter how fast they are traveling. Whether your feet are firmly planted on Earth or aboard a spacecraft speeding toward a far planet, you'd measure the exact same pace to light's motion, 299,792 kilometers (186,282 miles) per second.
How is that possible? It seems to go against common sense. But Einstein ingeniously deduced that if the speed of light is identical for all observers, no matter what their state of motion, then something else has to give. And that something else was absolute time and space. With his special theory of relativity, Einstein completely altered the traditional perspective of classical physics that had been firmly established by his illustrious predecessor. “Newton, forgive me,” said Einstein in his autobiographical notes. “You found the only way which, in your age, was just about possible for a man of highest thought—and creative power.” In Newton's world, there was one universal clock and common reference frame, which made time and space the same for one and all throughout the cosmos. But that scheme no longer held. Instead, space and time were now “relative,” flowing differently for each one of us depending on our motion. Einstein intuited that length and time are adjustable. If two observers are uniformly speeding either toward or away from each other, each will measure space shrinking and time proceeding slower for the other. Their clocks and yardsticks will not match up, as they did under Newton's laws. The only thing that they will agree on is the speed of light, a universal constant that remains unchanged for both travelers. The reason this seems counterintuitive is that we can't readily discern these differences in length and time in our rather humdrum surroundings. The changes are only apparent when the speeds between two objects are enormous, a sizable fraction of the velocity of light.
Soon Einstein was not satisfied with that adjustment alone. Special relativity was just that—special. It could only explain the properties of objects moving at an unvarying velocity. But that restricted its use to a great extent. Most events in nature don't behave so methodically. What if something were speeding up, slowing down, or changing direction? What if an object were accelerating under the force of gravity? Einstein knew that he had to develop a more general theory to deal with these situations, and he struggled with the problem for nearly a decade. It was a formidable job, as he had to do nothing less than recast Newton's venerable laws of gravity in the light of relativity.
For years success eluded him as he struggled to figure out how to make his equations truly universal and still reproduce Newton's law of gravity for the simplest cases, when gravity was weak and velocities were low. After all, Einstein couldn't just throw out a law that had been time-tested for more than two centuries. His new theory had to agree very closely with Newton's in the everyday realm where physicists had long been conducting experiments, a place where space-time distortions were too small to be overt. But then the theory would have to merge smoothly into either the intense gravity or high-velocity regimes in which the strange effects of relativity at last become obvious. “In all my life I have labored not nearly as hard,” he wrote a colleague in the midst of his deliberations. “… Compared with this problem, the original relativity is child's play.”
The breakthrough for the thirty-six-year-old physicist finally came in November 1915. Over that month Einstein reported weekly to the Prussian Academy of Sciences on his final progress toward a new theory of gravitation. A key moment arrived in mid month, when he was able to successfully explain a small displacement in the orbit of Mercury, a nagging mystery to astronomers for decades. Einstein later remarked that he had palpitations of the heart upon seeing this result: “I was beside myself with ecstasy for days.”
Complete success arrived on November 25, the day he presented his concluding paper. In this culminating talk, Einstein presented the decisive modifications that allowed him to secure a comprehensive theory. Written in the terse notation of tensor calculus—shorthand for a larger set of more complex functions—the general theory of relativity looks deceptively like a simple algebraic equation. It fits on one line and is the embodiment of mathematical elegance:
Ruv − ½guvR = −kTuv
On the left side are quantities that describe the gravitational field as the geometry of space-time. In fact, the Rs denote how much spacetime is curved. On the right side is a representation of mass-energy and how it is distributed. The equal sign sets up an intimate relationship between these two entities. As Princeton physicist John Archibald Wheeler liked to put it, “Spacetime tells mass how to move and mass tells spacetime how to curve.”
Einstein showed that the three dimensions of space and the additional dimension of time join up to form a real, palpable object. While it's impossible for us to visualize these four dimensions, it can be pictured in three. Think of space-time as a boundless rubber sheet. Masses, such as a star or planet, then indent this flexible mat, curving space-time. The more massive the object, the deeper the depression. Planets thus circle the Sun not because they are held by invisible tendrils of force, as Newton had us think, but because they are caught in the natural hollow formed by the Sun in four-dimensional space-time, much as a rolling marble would circle around a bowling ball sitting in a trampoline. With this image in mind, the pull of gravity could now be easily explained; it's merely matter sliding like a downhill skier along the undulations of space-time. When Einstein's younger son, Eduard, later asked his father why he was so famous, Einstein singled out this elegant and lucid illustration of gravity as curving space-time. “When a blind beetle crawls over the surface of a curved branch, it doesn't notice that the track it has covered is indeed curved,” he explained. “I was lucky enough to notice what the beetle didn't notice.”
This realization was why Einstein was so excited by his successful result regarding the planet Mercury. It was clear evidence of this fantastic new image of gravity, its geometric representation. His insight centered on the fact that planets do not orbit the Sun in perfect circles but rather in ellipses, one end being slightly closer to the Sun than the other. And it was long known that the point of Mercury's orbit that is closest to the Sun—its perihelion—shifts around over time due to the combined gravitational tugs of the other planets. But there is an added shift—an extra 43 seconds of arc (or arcseconds) per century—that could never be adequately explained. Astronomers had even postulated an undiscovered planet called Vulcan—even closer to the Sun than Mercury—to explain the anomaly.
Here's where the relativistic geometry makes a difference: Because Mercury is situated so close to the Sun, whose mass has created a sizable space-time crater, it has more of a “dip” to contend with, more so than the other planets. Einstein declared that the added shift in Mercury's orbit was caused solely by Mercury's proximity to the Sun, not by some yet-to-be-observed inner planet. This wasn't just a vague prediction; the equations of general relativity accounted for Mercury's extra 43 arcseconds of shift per century with utmost precision.
Arthur Eddington, for one, was immediately smitten by Einstein's groundbreaking opus. “Whether the theory ultimately proves to be correct or not, it claims attention as being one of the most beautiful examples of the power of general mathematical reasoning,” he wrote in his account of general relativity, the first book on the subject to appear in English. With Eddington acting as Einstein's translator and champion, the two were often linked in people's minds. An accomplished popularizer of science, Eddington said that Einstein had taken “Newton's plant, which had outgrown its pot, and transplanted it to a more open field.” Eddington was becoming so proficient at explaining relativity that “people seem to forget that I am an astronomer and that relativity is only a side issue,” he lamented after one wearying interview with reporters.
Arthur Eddington (AIP Emilio Segrè Visual Archives)
For Eddington to serve as a spokesman for a radical new theory was somewhat out of character for him. He was usually reserved to the point of shyness, so shy, said physicist Hermann Bondi, that “he couldn't talk at all… When anybody was with him … he played with his pipe, and emptied it and re-stuffed it, and occasionally said a word about the weather.” A thin man of average height but with penetrating eyes, he lived with his sister, who served as homemaker and hostess at their Cambridge Observatory residence. A devout Quaker and pacifist, Eddington remained at Cambridge University in Great Britain during World War I, having been declared valuable to the “national interest” at his university post.
As both an astronomer and a theorist, Eddington divined early on the revolutionary significance of Einstein's ideas: that the general theory of relativity was offering a means to comprehend the workings of the cosmos within a rational and mathematical framework. While Newton's laws were fine for predicting the behavior of comets, planets, and stars, only general relativity could deal with the immensity of space-time as a whole. And at the moment Eddington was beginning to work on a translation of general relativity for his colleagues, Einstein was already at work applying his revolutionary new theory to the universe at large.
For Newton, space was eternally at rest, merely an inert and empty container, a three-dimensional stage through which objects moved about. But general relativity changed all that. Now the stage itself became an active player, since the matter within the cosmos sculpts its overall curvature. With this new insight into gravity, physicists could at last make predictions about the universe's behavior, an innovation that moved cosmology out of the realm of philosophy, its long-standing home, and transformed it into a working science.
Einstein was the first to do this. In 1917, just as Shapley in California was revamping the Milky Way, he published a paper in Germany titled “Cosmological Considerations Arising from the General Theory of Relativity.” In it he explored how his new gravitational ideas could be used to determine the universe's behavior. Einstein had always been attracted to that age-old question: Is the universe infinite or finite in extension? “I compare space to a cloth…one can observe a certain portion,” he mused. “… We speculate how to extrapolate the cloth, what holds its tangential tension in equilibrium…whether it is infinitely extended, or finite and closed.” Einstein decided that the universe was closed, what is also referred to as a spherical universe, the four-dimensional equivalent of a spherical Earth. Though this shape has neither a beginning nor an end, its volume is finite. Travel forward through it long enough and you return right back to your starting point, just as you would circumnavigating our globe. In this scheme matter is so plentiful that space-time bends profoundly, so much that it literally wraps itself up into a hyperdimensional ball. Recognizing how frightfully odd this sounded, Einstein told a friend, “It exposes me to the danger of being confined to a madhouse.” But he stuck with this strange notion, as it helped him get around other problems in applying general relativity to the cosmos. Einstein also preferred this model because, given his astronomical knowledge at the time, he assumed the universe was filled with matter and stable. In 1917 it certainly appeared to him to be steady and enduring. Truth be told, he liked the idea of an immutable cosmos, a large collection of stars fixed forever in the void.
From a theorist's perspective, this choice was mathematically beautiful, but it also presented a problem. Even Newton knew that matter distributed throughout a finite space would eventually coalesce into larger and larger lumps. Stellar objects would be gravitationally drawn to one another, closer and closer over time. Ultimately, the universe would collapse under the inescapable pull of gravity. So, to avoid this cosmic calamity and match his theory with then-accepted astronomical observations, Einstein altered his famous equation, adding the term λ (the Greek letter lambda), a fudge factor that came to be called the “cosmological constant.” This new ingredient was an added energy that permeated empty space and exerted an outward “pressure” on it. This repulsive field—a kind of antigravity, actually—exactly balanced the inward gravitational attraction of all the matter in his closed universe, keeping it from moving. As a result, the universe remained immobile, “as required by the fact of the small velocities of the stars,” wrote Einstein in his classic 1917 paper.
Willem de Sitter
(Courtesy of the Archives, California
Institute of Technology)
Others soon followed up on Einstein's cosmological endeavor, most important Willem de Sitter. The esteemed Dutch astronomer, a tall and slender man with a neatly trimmed Vandyke beard, started keeping track of general relativity's development as early as 1911 and was one of the first to recognize its deep significance to astronomy. After meeting with Einstein in Leiden on several occasions in 1916, discussions in fact that inspired Einstein to conceive his spherical universe, de Sitter soon corresponded with Eddington on the subject. Intrigued by de Sitter's insights, Eddington asked him to write up his impressions of general relativity for the Monthly Notices of the Royal Astronomical Society, which resulted in three long papers on the topic, the first articles to make Einstein's accomplishment widely known to scientists outside Germany. De Sitter was obviously stimulated by the assignment, for in his third paper he offered up his own cosmological solution to the equations of general relativity, one that was very different from Einstein's.
When scientists originate an equation to describe some phenomenon, their job is far from done. They must still solve the equation—in the case of general relativity, figure out what values for those Rs and Ts make the equation come out right. This is a tall order. So, to progress, a researcher will often introduce a simplifying assumption about the equation that makes the problem easier. If a solution is found in this way—and there is no guarantee—the scientist trusts it will shed some light on the overall problem, leading them to a more complete understanding.
What de Sitter assumed was that the universe contained no matter. He discovered that Einstein's equation could be solved if he imagined that the universe was both stable and empty. On the face of it, this seemed like a ludicrous assumption, but de Sitter wondered if cosmic densities were so low that the universe could be considered essentially barren. By making this conjecture he was able to construct a model of space-time in which “the frequency of light-vibrations diminishes.” That is, light waves get longer (more red) with increasing distance from their source. The unique properties of space-time that arose in his solution demanded it. Einstein was not up on the latest astronomical news, but de Sitter was. In fact, he would soon be director of the Leiden Observatory, in the Netherlands. He was very aware that V. M. Slipher, at the Lowell Observatory, had recently discovered some spiral nebulae seemingly racing away from the Milky Way—and at very high velocities as measured by their redshifts. De Sitter was one of the few at the time who was sure that the spiral nebulae being sighted by astronomers in ever greater numbers were probably “amongst the most distant objects we know,” indisputably located beyond the Milky Way. And he surmised that their tendency to display appreciable redshifts could be proof of his model. In his paper, he suggested that the nebulae might only appear to be moving outward because their light waves were getting longer and longer (hence redder and redder) as the light traveled toward Earth. This set up the illusion of movement.
On the other hand, there was another way to interpret the effects in de Sitter's universe: Any bit of matter dropped inside its space-time would immediately fly off. That was another possible reason for the red-shifts Slipher was noticing. Eddington liked to say that “Einstein's universe contains matter but no motion and de Sitter's contains motion but no matter.”
Before the publication of his bizarre yet fascinating solution, de Sitter exchanged a number of letters with Einstein arguing over its details. Einstein was clearly flummoxed by de Sitter's quirky take on the universe. It “does not make sense to me,” he wrote. Where was the “world material” in his cosmos, where were the stars? It didn't seem based in reality. In Einstein's eyes, de Sitter's solution was physically impossible. The properties of space could not be determined, he believed, without the presence of matter.
Albert Einstein and Willem de Sitter working out a problem
at the Mount Wilson Observatory's Pasadena headquarters in 1932
De Sitter was certainly making a huge assumption by considering a cosmic density so low that the universe could be regarded as devoid of matter. But what was exciting about his model was that it was testable. If distances to the spiral nebulae could be measured precisely, then astronomers would be able to see if the redshifts truly increased “systematically,” as de Sitter noted in his paper. That is, the more distant a spiral, the larger its redshift. But in 1917 carrying out such rigorous measurements was a pipe dream. At that time astronomers were still not settled on what a spiral was, much less able to figure out its exact distance.
Besides, few astronomers were paying attention to Einstein's theory as yet. World War I had kept Einstein's work from being widely circulated outside Germany, and when astronomers did hear of it, they weren't quite sure what to make of its unconventional and perplexing view of gravity. George Hale, like many astronomers at the time who were trained to observe rather than to tinker with mathematical equations, said he feared “it will always remain beyond my grasp.” All of that changed, though, once the findings of a British solar-eclipse expedition in 1919 transformed the name of Einstein, the former Swiss patent clerk, into a synonym for genius.
At the time Einstein was working on general relativity, he had early on suggested a specific test that astronomers could perform to confirm his predicted curvatures in space-time: Photograph a field of stars at night, then for comparison photograph those same stars when they pass near the Sun's limb during a solar eclipse. A beam of starlight passing right by the Sun would be gravitationally attracted to the Sun and get bent, making it appear that the star has shifted its standard position on the celestial sky, the position it would have if the Sun were in another part of the heavens. In 1911 he computed a bending of 0.83 arcseconds, the same arising from Newton's laws alone. But a few years later, once his final theory was in place, Einstein doubled his predicted bending. The extra contribution, Einstein figured out, occurs due to the Sun's enormous mass warping space-time. He calculated that a stellar ray just grazing the Sun would get deflected by 1.7 arcseconds (a thousandth the width of the Moon).
Three solar-eclipse expeditions were launched prior to 1919 to detect this light bending but were unsuccessful due to either bad weather or the ongoing war. The results of a fourth effort, an American endeavor led by Lick astronomers W. W. Campbell and Heber Curtis, were plagued by data comparison problems and so were never published. That was a fortunate turn of events for Einstein. The shaky American results went against him, and some of the other expeditions were carried out when his theory, not yet fully developed, was predicting that smaller, incorrect deflection.
That's why scientists paid keen attention to British astronomers when they announced they would give it a try in 1919 during a favorable solar eclipse whose path crossed South America and continued over to central Africa. The eclipse was taking place against a particularly rich background of stars, the Hyades cluster, which offered excellent opportunities to detect a star's shift. Sir Frank Dyson, Great Britain's astronomer royal, first pointed out this fortunate occurrence more than two years earlier. “This should serve for an ample verification, or the contrary, of Einstein's theory,” he noted at the time. And as the victors in World War I, the British had the necessary funding to organize and carry out the intricate venture.
On the evening before sailing, Eddington and his eclipse companion, E. T Cottingham, joined Dyson in his study. The discussion turned to the amount of deflection expected from classical Newtonian theory compared to Einstein's predicted value, which was twice as great. “What will it mean,” asked Cottingham playfully, “if we get double the Einstein deflection?” Dyson replied, “Then Eddington will go mad and you will have to come home alone!”
The next day Eddington and his assistant began their journey to the tiny isle of Principe, situated 140 miles off the coast of West Africa, a favorable site in the path of the eclipse. And to improve the venture's chances for a clear-weather view, two other astronomers traveled to the village of Sobral in the Amazon jungle of northern Brazil. On the day of the eclipse, May 29, a violent morning rainstorm almost doomed the Principe crew's operations. But by noon, the deluge ended and an hour and a half later they got their first glimpse of the Sun, already partially covered by the Moon. Too busy changing plates during totality, Eddington had only one chance, halfway through, to view the Sun's dark visage. “We are conscious only of the weird half-light of the landscape and the hush of nature, broken by the calls of the observers, and beat of the metronome ticking out the 302 seconds of totality,” he later recalled of the adventure.
The astronomers in Sobral were more fortunate. There they had two instruments and better weather. With their astrographic telescope they clicked off sixteen photos, and eight more were taken with a 4-inch scope. On Principe, Eddington and Cottingham, too, took sixteen photographs, but most ultimately turned out useless because of the intervening clouds. For several days after the eclipse, Eddington spent the daytime hours taking a first stab at measuring the star images on the plates that did turn out well. Upon examining the preliminary results, he turned to his colleague and exclaimed, “Cottingham, you won't have to go home alone.” He saw evidence that the streams of starlight had indeed bent around the darkened Sun according to Einstein's rules.
At a dinner soon after his return to England, Eddington entertained some fellow astronomers with a poem in the style of the Rubáiyát. “One thing is certain, and the rest debate—light-rays, when near the Sun, DO NOT GO STRAIGHT” was his rousing finale. In November the results of the expedition were officially reported at a special joint meeting in London of the Royal Society and the Royal Astronomical Society. Dyson spoke on behalf of the participants and behind him, almost like a stage setting, hung a picture of Isaac Newton, whose historic law of gravitation was undergoing its first modification. The best results supporting Einstein came from the Sobral 4-inch telescope. From its plates, the Britishers measured a starlight deflection of 1.98 arcseconds, a little on the high side of Einstein's prediction. The poorer images from Principe suggested a bending of 1.61 arcseconds, just below what Einstein calculated. Viewed together, though, Einstein was deemed a winner. These were the results that Eddington and Dyson stressed in their reports, which were widely hailed in newspaper headlines worldwide, turning Einstein into an overnight celebrity. “LIGHTS ALL ASKEW IN THE HEAVENS, Men of Science More or Less Agog Over Results of Eclipse Observations… Stars Not Where They Seemed or Were Calculated to be, but Nobody Need Worry,” blared the New York Times. Suddenly the public's attention was riveted to all things relative. Awed by the contributions scientists had made in the war effort, the public was highly receptive to hear more from the physics frontier—at least until their attention was diverted by the tomb of a young Egyptian pharaoh named Tutankhamen (“King Tut”) found a few years later almost completely intact.
Often neglected in the recountings of the famous 1919 solar-eclipse expedition was the team's largest data set from the Sobral astrographic telescope, which indicated a deflection of 0.93 arcseconds, in favor of Sir Isaac Newton. Because of various technical problems with the Sobral scope, including a blurring of its images, the British team decided to downplay that instrument's results. Eddington admitted he was unscientifically rooting for Einstein, but his instincts to reject the astrographic telescope results turned out to be good in the end. Campbell headed up another solar-eclipse expedition in 1922, which arrived at similar results and further confirmed Einstein's theory. When asked what he had been expecting, Campbell replied in all seriousness, “I hoped it would not be true.” Relativity's thoroughly new vision of space and time, coupled with its complexity, made even several leading scientists reluctant to accept its predictions. Those primarily trained in classical physics were quite leery of general relativity's strange outlook on the force of gravity and wondered if the light-bending was actually a refraction effect in the Sun's atmosphere or perhaps was due to a physical distortion of the photographic plate from imaging the hot solar corona. Heber Curtis, who met Einstein during his first visit to the United States, was certainly no fan of relativity. “We met in quick succession Their Eminences, the Prince of Monaco, Dr. Einstein and President Harding, and were photographed in a group on the White House lawn,” Curtis wrote Campbell soon after the meeting. Curtis, who was still convinced he had proven Einstein wrong with his flawed 1918 expedition results, would have been glad to see someone join him in overturning Einstein. “He surely looks like the fourth dimension!” joked Curtis about the German phenom. “Face is somewhat sallow and yellowish, redeemed by very keen bright eyes. But wears his hair a la [Polish pianist Ignacy] Paderewski in narrow greasy curls of small diameter and four or five inches long.”
Even a full decade after general relativity was introduced, many scientists were still resisting Einstein's new view of the universe. At the National Academy of Sciences meeting in Washington in 1925, physicist Dayton Miller of the Case School of Applied Science in Cleveland announced he had seen evidence of an “ether drag,” the speed of light changing with the motion of Earth. According to one conference attendee, this report was a “bombshell…which quite blew up the meeting of the Academy and got more applause than anything that happened…[disturbing] the relativists in general.”
Einstein supporters were enraged that doubts over relativity still lingered at all. “I am really getting pretty tired of the fundamentalist's attitude of the opponents of relativity,” said Henry Norris Russell in response to Miller's bolt from the blue. “Their psychology seems to me to be exactly similar to that of the most conservative theologians.” In time, though, Miller's experiments proved faulty, and astronomers would eventually have to face up to the new cosmic order.